Understanding Δx: The Meaning and Importance of Uppercase Delta in Math

[MarcAlexander]

So I'm aware that the triangle is uppercase delta which means the difference between: 10\Delta5=5

But what does Δx mean?

 

[DrGreg]

It means the difference between two values of the variable x, between two specified events.

 

[noxxo]

It means the change in x. For x(at event 1) = 2 and x(at event 2) = 4 : delta x = 4-2 = 2

 

[nonequilibrium]

sometimes it is also used to refer to uncertainty in the variable x
what kind of "uncertainty" depends on the context: experimental, or pertaining to it being defined, ...

 

[brocks]

So I'm aware that the triangle is uppercase delta which means the difference between: 10\Delta5=5

Actually I've never seen that use of it. I'm not saying it's wrong, but it's unusual.

But in elementary math texts, \Deltax means the amount of change in the variable x. For example, the slope of a line is \Deltay/\Deltax, i.e. the change in y divided by the change in x, for any two points on the line.

When you learn calculus, you will see that the instantaneous velocity of an object traveling along the x-axis is the limit of the displacement divided by the elapsed time, \Deltax/\Deltat, as \Deltat approaches zero.

 

[Allenman]

It's already been answered pretty good. But just to clarify:

\Deltax = x_{2}-x_{1}

or the slope of a function:
\frac{\Delta y}{\Delta x} = \frac{y_{2} -y_{1}}{x_{2}-x_{1}}

Which you'll find to be very similar to the definition of a derivative in calculus:
\frac{\delta y}{\delta x} which basically means (difference in y)/(difference in x)

Capital delta is looking for a specific answer (most times) while lower case is looking for another equation (most times).

 

[MarcAlexander]

It's already been answered pretty good. But just to clarify:

\Deltax = x_{2}-x_{1}

or the slope of a function:
\frac{\Delta y}{\Delta x} = \frac{y_{2} -y_{1}}{x_{2}-x_{1}}

Which you'll find to be very similar to the definition of a derivative in calculus:
\frac{\delta y}{\delta x} which basically means (difference in y)/(difference in x)

Capital delta is looking for a specific answer (most times) while lower case is looking for another equation (most times).

What book would provide me with a quick reference to the use of greek letters in Physics?

 

[Pythagorean]

Most symbols have different meanings in different contexts. Pi is one of the few symbols that has a consistent meaning.

 

[Allenman]

What book would provide me with a quick reference to the use of greek letters in Physics?

this is helpful:
http://www.dpi.state.nc.us/docs/accountability/testing/eoc/Physics/physicsreferencetable.pdf

This has all the Greek symbols:
http://en.wikibooks.org/wiki/Physics_Study_Guide/Greek_alphabet